{
  "id": "2401.07168",
  "version": "v1",
  "published": "2024-01-13T22:40:21.000Z",
  "updated": "2024-01-13T22:40:21.000Z",
  "title": "Assouad spectrum of Gatzouras-Lalley carpets",
  "authors": [
    "Amlan Banaji",
    "Jonathan M. Fraser",
    "István Kolossváry",
    "Alex Rutar"
  ],
  "comment": "42 pages, 6 figures",
  "categories": [
    "math.DS",
    "math.CA",
    "math.MG"
  ],
  "abstract": "We study the fine local scaling properties of a class of self-affine fractal sets called Gatzouras-Lalley carpets. More precisely, we establish a formula for the Assouad spectrum of all Gatzouras-Lalley carpets as the concave conjugate of an explicit piecewise-analytic function combined with a simple parameter change. Our formula implies a number of novel properties for the Assouad spectrum not previously observed for dynamically invariant sets; in particular, the Assouad spectrum can be a non-trivial differentiable function on the entire domain $(0,1)$ and can be strictly concave on open intervals. Our proof introduces a general framework for covering arguments using techniques developed in the context of multifractal analysis, including the method of types from large deviations theory and Lagrange duality from optimisation theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-13T22:40:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "37C45",
      "49N15"
    ],
    "keywords": [
      "assouad spectrum",
      "gatzouras-lalley carpets",
      "large deviations theory",
      "self-affine fractal sets",
      "explicit piecewise-analytic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}